173.26/44.26 YES 173.26/44.27 173.26/44.27 Problem: 173.26/44.27 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.27 c(a(x1)) -> a(c(x1)) 173.26/44.27 c(b(x1)) -> b(a(x1)) 173.26/44.27 L(a(a(x1))) -> L(a(b(c(x1)))) 173.26/44.27 c(R(x1)) -> b(a(R(x1))) 173.26/44.27 173.26/44.27 Proof: 173.26/44.27 DP Processor: 173.26/44.27 DPs: 173.26/44.27 b#(a(a(x1))) -> c#(x1) 173.26/44.27 b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 c#(a(x1)) -> c#(x1) 173.26/44.27 c#(b(x1)) -> b#(a(x1)) 173.26/44.27 L#(a(a(x1))) -> c#(x1) 173.26/44.27 L#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) 173.26/44.27 c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 TRS: 173.26/44.27 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.27 c(a(x1)) -> a(c(x1)) 173.26/44.27 c(b(x1)) -> b(a(x1)) 173.26/44.27 L(a(a(x1))) -> L(a(b(c(x1)))) 173.26/44.27 c(R(x1)) -> b(a(R(x1))) 173.26/44.27 TDG Processor: 173.26/44.27 DPs: 173.26/44.27 b#(a(a(x1))) -> c#(x1) 173.26/44.27 b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 c#(a(x1)) -> c#(x1) 173.26/44.27 c#(b(x1)) -> b#(a(x1)) 173.26/44.27 L#(a(a(x1))) -> c#(x1) 173.26/44.27 L#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) 173.26/44.27 c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 TRS: 173.26/44.27 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.27 c(a(x1)) -> a(c(x1)) 173.26/44.27 c(b(x1)) -> b(a(x1)) 173.26/44.27 L(a(a(x1))) -> L(a(b(c(x1)))) 173.26/44.27 c(R(x1)) -> b(a(R(x1))) 173.26/44.27 graph: 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) -> 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> c#(x1) 173.26/44.27 L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 L#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) 173.26/44.27 L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) 173.26/44.27 L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) 173.26/44.27 c#(R(x1)) -> b#(a(R(x1))) -> b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 c#(R(x1)) -> b#(a(R(x1))) -> b#(a(a(x1))) -> c#(x1) 173.26/44.27 c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) 173.26/44.27 c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) 173.26/44.27 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 173.26/44.27 b#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) 173.26/44.27 b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) 173.26/44.27 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) 173.26/44.27 EDG Processor: 173.26/44.27 DPs: 173.26/44.27 b#(a(a(x1))) -> c#(x1) 173.26/44.27 b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 c#(a(x1)) -> c#(x1) 173.26/44.27 c#(b(x1)) -> b#(a(x1)) 173.26/44.27 L#(a(a(x1))) -> c#(x1) 173.26/44.27 L#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) 173.26/44.27 c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 TRS: 173.26/44.27 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.27 c(a(x1)) -> a(c(x1)) 173.26/44.27 c(b(x1)) -> b(a(x1)) 173.26/44.27 L(a(a(x1))) -> L(a(b(c(x1)))) 173.26/44.27 c(R(x1)) -> b(a(R(x1))) 173.26/44.27 graph: 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> c#(x1) 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> L#(a(b(c(x1)))) 173.26/44.27 L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) 173.26/44.27 L#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) 173.26/44.27 L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) 173.26/44.27 L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) 173.26/44.27 c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 173.26/44.27 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) 173.26/44.27 c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) 173.26/44.27 b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) 173.26/44.27 b#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) 173.26/44.27 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) 173.26/44.27 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 173.26/44.27 SCC Processor: 173.26/44.27 #sccs: 2 173.26/44.27 #rules: 5 173.26/44.27 #arcs: 18/64 173.26/44.27 DPs: 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) 173.26/44.27 TRS: 173.26/44.27 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.27 c(a(x1)) -> a(c(x1)) 173.26/44.27 c(b(x1)) -> b(a(x1)) 173.26/44.27 L(a(a(x1))) -> L(a(b(c(x1)))) 173.26/44.27 c(R(x1)) -> b(a(R(x1))) 173.26/44.27 Usable Rule Processor: 173.26/44.27 DPs: 173.26/44.27 L#(a(a(x1))) -> L#(a(b(c(x1)))) 173.26/44.27 TRS: 173.26/44.27 c(a(x1)) -> a(c(x1)) 173.26/44.27 c(b(x1)) -> b(a(x1)) 173.26/44.27 c(R(x1)) -> b(a(R(x1))) 173.26/44.27 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.27 Arctic Interpretation Processor: 173.26/44.27 dimension: 1 173.26/44.27 usable rules: 173.26/44.28 c(a(x1)) -> a(c(x1)) 173.26/44.28 c(b(x1)) -> b(a(x1)) 173.26/44.28 c(R(x1)) -> b(a(R(x1))) 173.26/44.28 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.28 interpretation: 173.26/44.28 [L#](x0) = x0 + 0, 173.26/44.28 173.26/44.28 [R](x0) = 0, 173.26/44.28 173.26/44.28 [c](x0) = 1x0 + 1, 173.26/44.28 173.26/44.28 [b](x0) = -1x0 + 0, 173.26/44.28 173.26/44.28 [a](x0) = 1x0 + 1 173.26/44.28 orientation: 173.26/44.28 L#(a(a(x1))) = 2x1 + 2 >= 1x1 + 1 = L#(a(b(c(x1)))) 173.26/44.28 173.26/44.28 c(a(x1)) = 2x1 + 2 >= 2x1 + 2 = a(c(x1)) 173.26/44.28 173.26/44.28 c(b(x1)) = x1 + 1 >= x1 + 0 = b(a(x1)) 173.26/44.28 173.26/44.28 c(R(x1)) = 1 >= 0 = b(a(R(x1))) 173.26/44.28 173.26/44.28 b(a(a(x1))) = 1x1 + 1 >= 1x1 + 1 = a(b(c(x1))) 173.26/44.28 problem: 173.26/44.28 DPs: 173.26/44.28 173.26/44.28 TRS: 173.26/44.28 c(a(x1)) -> a(c(x1)) 173.26/44.28 c(b(x1)) -> b(a(x1)) 173.26/44.28 c(R(x1)) -> b(a(R(x1))) 173.26/44.28 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.28 Qed 173.26/44.28 173.26/44.28 DPs: 173.26/44.28 b#(a(a(x1))) -> b#(c(x1)) 173.26/44.28 b#(a(a(x1))) -> c#(x1) 173.26/44.28 c#(b(x1)) -> b#(a(x1)) 173.26/44.28 c#(a(x1)) -> c#(x1) 173.26/44.28 TRS: 173.26/44.28 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.28 c(a(x1)) -> a(c(x1)) 173.26/44.28 c(b(x1)) -> b(a(x1)) 173.26/44.28 L(a(a(x1))) -> L(a(b(c(x1)))) 173.26/44.28 c(R(x1)) -> b(a(R(x1))) 173.26/44.28 Usable Rule Processor: 173.26/44.28 DPs: 173.26/44.28 b#(a(a(x1))) -> b#(c(x1)) 173.26/44.28 b#(a(a(x1))) -> c#(x1) 173.26/44.28 c#(b(x1)) -> b#(a(x1)) 173.26/44.28 c#(a(x1)) -> c#(x1) 173.26/44.28 TRS: 173.26/44.28 c(a(x1)) -> a(c(x1)) 173.26/44.28 c(b(x1)) -> b(a(x1)) 173.26/44.28 c(R(x1)) -> b(a(R(x1))) 173.26/44.28 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.28 Arctic Interpretation Processor: 173.26/44.28 dimension: 1 173.26/44.28 usable rules: 173.26/44.28 c(a(x1)) -> a(c(x1)) 173.26/44.28 c(b(x1)) -> b(a(x1)) 173.26/44.28 c(R(x1)) -> b(a(R(x1))) 173.26/44.28 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.28 interpretation: 173.26/44.28 [c#](x0) = 2x0, 173.26/44.28 173.26/44.28 [b#](x0) = x0, 173.26/44.28 173.26/44.28 [R](x0) = x0, 173.26/44.28 173.26/44.28 [c](x0) = 1x0, 173.26/44.28 173.26/44.28 [b](x0) = x0, 173.26/44.28 173.26/44.28 [a](x0) = 1x0 173.26/44.28 orientation: 173.26/44.28 b#(a(a(x1))) = 2x1 >= 1x1 = b#(c(x1)) 173.26/44.28 173.26/44.28 b#(a(a(x1))) = 2x1 >= 2x1 = c#(x1) 173.26/44.28 173.26/44.28 c#(b(x1)) = 2x1 >= 1x1 = b#(a(x1)) 173.26/44.28 173.26/44.28 c#(a(x1)) = 3x1 >= 2x1 = c#(x1) 173.26/44.28 173.26/44.28 c(a(x1)) = 2x1 >= 2x1 = a(c(x1)) 173.26/44.28 173.26/44.28 c(b(x1)) = 1x1 >= 1x1 = b(a(x1)) 173.26/44.28 173.26/44.28 c(R(x1)) = 1x1 >= 1x1 = b(a(R(x1))) 173.26/44.28 173.26/44.28 b(a(a(x1))) = 2x1 >= 2x1 = a(b(c(x1))) 173.26/44.28 problem: 173.26/44.28 DPs: 173.26/44.28 b#(a(a(x1))) -> c#(x1) 173.26/44.28 TRS: 173.26/44.28 c(a(x1)) -> a(c(x1)) 173.26/44.28 c(b(x1)) -> b(a(x1)) 173.26/44.28 c(R(x1)) -> b(a(R(x1))) 173.26/44.28 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.28 Restore Modifier: 173.26/44.28 DPs: 173.26/44.28 b#(a(a(x1))) -> c#(x1) 173.26/44.28 TRS: 173.26/44.28 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.28 c(a(x1)) -> a(c(x1)) 173.26/44.28 c(b(x1)) -> b(a(x1)) 173.26/44.28 L(a(a(x1))) -> L(a(b(c(x1)))) 173.26/44.28 c(R(x1)) -> b(a(R(x1))) 173.26/44.28 EDG Processor: 173.26/44.28 DPs: 173.26/44.28 b#(a(a(x1))) -> c#(x1) 173.26/44.28 TRS: 173.26/44.28 b(a(a(x1))) -> a(b(c(x1))) 173.26/44.28 c(a(x1)) -> a(c(x1)) 173.26/44.28 c(b(x1)) -> b(a(x1)) 173.26/44.28 L(a(a(x1))) -> L(a(b(c(x1)))) 173.26/44.28 c(R(x1)) -> b(a(R(x1))) 173.26/44.28 graph: 173.26/44.28 173.26/44.28 SCC Processor: 173.26/44.28 #sccs: 0 173.26/44.28 #rules: 0 173.26/44.28 #arcs: 0/1 173.26/44.28 173.26/44.28 EOF